Nonlinear stability analysis of thin FGM annular spherical shells on elastic foundations under external pressure and thermal loads

•We investigated nonlinear stability analysis of FGM annular spherical shells.•The shell resting on elastic foundations.•The shell subjected by external pressure and thermal loads.•The classical thin shell theory and the stress function are used.•The nonlinear response of the shell is analyzed and discussed.

To increase the thermal resistance of various structural components in high-temperature environments, the present research deals with nonlinear stability analysis of thin annular spherical shells made of functionally graded materials (FGM) on elastic foundations under external pressure and temperature. Material properties are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Classical thin shell theory in terms of the shell deflection and the stress function is used to determine the buckling loads and nonlinear response of the FGM annular spherical shells. Galerkin method is applied to obtain closed – form of load – deflection paths. An analysis is carried out to show the effects of material, geometrical properties, elastic foundations and combination of external pressure and temperature on the nonlinear stability of the annular spherical shells.